Governing equations on differential form: Difference between revisions

@@ Line 210: / Line 210: @@
 and thus we end up with the energy equation on non-conservation differential form
-\begin{equation}
+<math display="block">
 \rho\frac{De_o}{Dt} + \nabla\cdot(p\mathbf{v}) = \rho\mathbf{f}\cdot\mathbf{v} + \dot{q}\rho
-\label{eq:governing:energy:non}
+</math>
-\end{equation}\\
-%\section*{The Governing Equations on Differential Non-Conservation Form}
+==== Summary ====
-%
-%\vspace*{1cm}
+Continuity:
-%
-%\noindent Continuity:
+<math display="block">
-%
+\frac{D\rho}{Dt}+\rho(\nabla\cdot\mathbf{v})=0
-%\begin{equation}
+</math>
-%\frac{D\rho}{Dt}+\rho(\nabla\cdot\mathbf{v})=0
-%\label{eq:governing:cont:non}
+Momentum:
-%\end{equation}\\
-%
+<math display="block">
-%\noindent Momentum:
+\frac{D\mathbf{v}}{Dt}+\frac{1}{\rho}\nabla p = \mathbf{f}
-%
+</math>
-%\begin{equation}
-%\frac{D\mathbf{v}}{Dt}+\frac{1}{\rho}\nabla p = \mathbf{f}
+Energy:
-%\label{eq:governing:mom:non}
-%\end{equation}\\
+<math display="block">
-%
+\rho\frac{De_o}{Dt} + \nabla\cdot(p\mathbf{v}) = \rho\mathbf{f}\cdot\mathbf{v} + \dot{q}\rho
-%\noindent Energy:
+</math>
-%
-%\begin{equation}
-%\rho\frac{De_o}{Dt} + \nabla\cdot(p\mathbf{v}) = \rho\mathbf{f}\cdot\mathbf{v} + \dot{q}\rho
-%\label{eq:governing:energy:non}
-%\end{equation}\\
 === Alternative Forms of the Energy Equation ===

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